FORUM Design for Recycling Evaluation and Efficient Alloy Modification Gabrielle Gaustad, Elsa Olivetti, and Randolph Kirchain Keywords: aluminum design for environment (DfE) industrial ecology mathematical programming scrap uncertainty Supplementary material is available on the JIE Web site Address correspondence to: Randolph Kirchain Massachusetts Institute of Technology 77 Massachusetts Avenue E38-432 Cambridge, MA 02139 [email protected]http://msl.mit.edu c 2010 by Yale University DOI: 10.1111/j.1530-9290.2010.00229.x Volume 14, Number 2 Summary As design for recycling becomes more broadly applied in mate- rial and product design, analytical tools to quantify the environ- mental implications of design choices will become a necessity. Currently, few systematic methods exist to measure and direct the metallurgical alloy design process to create alloys that are most able to be produced from scrap. This is due, in part, to the difficulty in evaluating such a context-dependent proper ty as recyclability of an alloy, which will depend on the types of scraps available to producers, the compositional character- istics of those scraps, their yield, and the alloy specification itself. This article explores the use of a chance-constrained based optimization model, similar to models used in opera- tional planning in secondary production today, to (1) charac- terize the challenge of developing recycling-friendly alloys due to the contextual sensitivity of recycling, (2) demonstrate how such models can be used to evaluate the potential scrap usage of alloys, and (3) explore the value of sensitivity analysis infor- mation to proactively identify effective alloy modifications that can drive increased potential scrap use. These objectives are demonstrated through two cases that involve the production of a broad range of alloys utilizing representative scraps from three classes of industrial end uses. 286 Journal of Industrial Ecology www.blackwellpublishing.com/jie
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Design for RecyclingEvaluation and Efficient Alloy Modification
Gabrielle Gaustad, Elsa Olivetti, and Randolph Kirchain
Keywords:
aluminumdesign for environment (DfE)industrial ecologymathematical programmingscrapuncertainty
Supplementary material is availableon the JIE Web site
Address correspondence to:Randolph KirchainMassachusetts Institute of Technology77 Massachusetts AvenueE38-432Cambridge, MA [email protected]://msl.mit.edu
As design for recycling becomes more broadly applied in mate-rial and product design, analytical tools to quantify the environ-mental implications of design choices will become a necessity.Currently, few systematic methods exist to measure and directthe metallurgical alloy design process to create alloys that aremost able to be produced from scrap. This is due, in part, tothe difficulty in evaluating such a context-dependent propertyas recyclability of an alloy, which will depend on the typesof scraps available to producers, the compositional character-istics of those scraps, their yield, and the alloy specificationitself. This article explores the use of a chance-constrainedbased optimization model, similar to models used in opera-tional planning in secondary production today, to (1) charac-terize the challenge of developing recycling-friendly alloys dueto the contextual sensitivity of recycling, (2) demonstrate howsuch models can be used to evaluate the potential scrap usageof alloys, and (3) explore the value of sensitivity analysis infor-mation to proactively identify effective alloy modifications thatcan drive increased potential scrap use. These objectives aredemonstrated through two cases that involve the productionof a broad range of alloys utilizing representative scraps fromthree classes of industrial end uses.
286 Journal of Industrial Ecology www.blackwellpublishing.com/jie
One of the key engineering challenges of the21st century is reducing the harmful effects asso-ciated with a growing population and the atten-dant flows of materials (Frosch and Gallopoulos1989; Graedel and Allenby 2003). The materi-als community is uniquely positioned to play acentral role in addressing these problems by fun-damentally changing the materials and processesused by society. For this to happen, materials ex-perts must begin to consider the environmentalimpacts of their design choices, and they will re-quire additional analytical tools to quantify thosebroader implications. This article begins to ad-dress this need for at least one element of a mate-rial’s environmental performance—the ability tobe produced from secondary resources. Materialsthat perform well in this regard are consideredto be “recycling-friendly.” We have chosen thisterm to avoid causing confusion with recyclable orrecyclability. In this article, recycling-friendly refersto an alloy that can use recycled aluminum inits production portfolio; high recyclability indicatesthat an alloy can be recycled into another alloyat end of life.
Figure 1 Primary and secondary energy usage for various materials in 1995 (Keoleian et al. 1997). Theinset shows U.S. consumption of various metals (Kelly et al. 2004). Mg = magnesium; Al = aluminum; Cu =copper; Pb = lead; Zn = zinc; PVC = polyvinyl chloride.
Metals Recycling: A Case of Aluminum
It is well known for many materials, particu-larly for metals, that substitution of primary withsecondary resources (i.e., those recovered frommanufacturing waste or end-of-life products) de-creases energy consumption and the attendantenvironmental burden (see figure 1). Aluminum,the material selected as a case study for this ar-ticle, serves as an excellent example due to thelarge energy differences between primary and sec-ondary production: 175 megajoules per kilogram(MJ/kg) for primary, compared to 10 to 20 MJ/kgfor secondary (Keoleian et al. 1997).1
This energy advantage creates a strong eco-nomic incentive to recycle. This benefit is man-ifest in the rapid growth in secondary aluminumproduction (see figure 2A; Kelly and Matos2006), which is far outpacing growth in primaryproduction. Despite these large energy savingsand the rise in secondary production, recycling isnot necessarily increasing in the United States.Studies (IAI 2005) have found that at least 34%of available end-of-life aluminum products arecurrently not recycled. More troubling is the gen-eral stagnancy or decrease in the recycling rate ofaluminum over the last few years (see figure 2B);
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Figure 2 A. Primary and secondary production of aluminum (Al) in the United States; in recent years,secondary production has outpaced the growth of primary production substantially (Kelly and Matos 2006).B. Recycling rate for aluminum in the United States from 1990 to 2005 (Kelly and Matos 2006). “Old” scrapis collected from end-of-life products, whereas “new” scrap (also called prompt) is generated duringfabrication and manufacturing.
the recycling rate hovers around 40%, with end-of-life or “old” scrap accounting for 35% of thatfigure. The remainder consists of “new” scrap,also called prompt, which comes from the manu-facturing process. Recycling end-of-life materialsis considerably more compositionally challeng-ing than recycling prompt scrap due to (1) thefact that the metal of interest is combined withother materials when made into a product and (2)contamination from end-of-life processing. Thiscontamination from both material combinationand processing can result in accumulation of un-desirable elements within the material stream,which can hamper further recycling (Kim et al.1997; Hatayama et al. 2007).
Along with the compositional challengesmentioned above, a wide variety of barriers pre-vent increased usage of recycled or scrap materi-als. One barrier that is the focus of this work isthe saturation of sinks, or products that can useor absorb scrap raw materials, for some recycledraw materials. To date, secondary production hasfocused on satisfying demand for compositionallyforgiving cast alloys and for the carefully designedalloy systems used for can stock. If secondary pro-duction is to sustain its growth trend, the alloysinks for secondary material also need to expand.In fact, several authors have commented on thepending limits of many traditional aluminum al-loy sinks for recycled material, in particular alu-minum castings (Aluminum Association alloydesignation 380)2 and wrought3 aluminum can
stock (Aluminum Association alloy designations3105, 3004, and 3104; Gesing 2004; Das 2006).
Other barriers noted in the literature that areindirectly addressed by this work include the fol-lowing: limited recycling by consumers (Wattset al. 1999; Morgan and Hughes 2006), uncer-tain scrap availability (Toto 2004), and the highcost of collection (Porter 2002; Calcott and Walls2005). To expand recycling, the field must re-move or reduce these disincentives to return,collect, and process secondary material (Wernickand Themelis 1998; Goodman et al. 2005). Al-though this article focuses on using alloy designto broaden usage opportunities for lower qual-ity scraps, increasing such usage opportunitiesshould increase demand for secondary materialand thereby influence the collection and recoveryof secondary materials. Studies on copper (Slade1980), steel (Aylen and Albertson 2006), andaluminum (Blomberg and Soderholm 2009) havefound that increasing demand for scraps results inincreasing scrap prices, as economic theory wouldpredict; this, in turn, increases scrap supply bymotivating more collection and recovery.
Fortunately, several technological strategies4
are possible to facilitate increased recycling inspite of these barriers. At the highest level,these include strategies that change (1) the formand composition of the returning scrap, (2) thecharacteristics of the process that converts scrapto finished goods, and (3) the specifications bywhich a finished good is judged acceptable. Most
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discussions in the literature focus on changes toproducts (including changes to product archi-tecture, joining, or materials selection) as de-sign for recycling (Kriwet et al. 1995; Pneuli andZussman 1997; Mok et al. 2006; Masanet andHorvath 2007). Although this may be the mostcritical, it seems prudent to examine the poten-tial role of each strategy in achieving the max-imum potential use of secondary materials. Toguide the development of any of these strategies,the engineer or technical decision maker must beable to evaluate the implications for recyclabil-ity. This article explores the use of a modelingframework to perform such an evaluation anddemonstrates its application to guiding one im-provement strategy—alloy design. As with anysystems issue, the most effective evaluation ap-proach simultaneously considers the interactionsof all available strategies across each stage of thematerial or product life cycle. Recent work sug-gests that this is becoming feasible (Reuter andVan Schaik 2008). If properly structured, suchcomprehensive models should be able to provideboth post facto and a priori information to guidethe alloy design process. Fortunately, one can ex-plore the implications of such tools using modelsof much smaller scope. To that end, the modelapplied herein is simple and incorporates onlysmall changes from operational batch-planningmodels used throughout much of the secondarymetals industry. These batch-planning models in-form decisions about what mix of raw materials,scraps included, to include to optimally output al-loys to specification. Despite this simplicity, thismodel is sufficient to demonstrate both of thegoals of this article. These are (1) the challengeof creating a broadly recycling-friendly alloy and(2) utilizing the potential of sensitivity analysisinformation to make the design process more ef-ficient. Once the issues of available informationand stakeholder alignment or modeling are ad-dressed, we can apply properly structured modelsof systemic scope to generate analogous insights.
The Question of Recycling-FriendlyAlloy Design
How to design alloys that are more recycling-friendly, or, in other words, more able to accom-modate scrap materials in their production port-
folios, is a challenging question. Industry expertsand literature have provided a variety of sugges-tions. A much-discussed strategy involves the de-velopment of single alloys that could meet theperformance requirements currently filled by mul-tiple alloys. For example, an alloy could replaceboth 5XXX and 6XXX wrought materials (withthe major alloying elements magnesium for 5XXXand silicon and magnesium for 6XXX) in trans-portation applications (Miller et al. 2000; Daset al. 2008). Some authors have even proposedlegislation or regulations to limit the number ofalloys that can be used in certain products, suchas cars or aircraft (Woodward 1997). Other sug-gestions involve modifying the forming and join-ing of aluminum—for example, replacing con-ventional welding with mechanical joining, laserwelding, or friction stir welding (Sutherland et al.2004). Specific suggestions concerning the modi-fications of alloys include using higher maximumcompositional specifications or lower minimumspecifications for certain elements that will notadversely affect alloy properties and translatingcompositional constraints to specifications basedon performance (Das 2006; Das et al. 2007). Noquantitative assessments of the efficacy of thesesuggestions on the ability of a recycler or recy-cling system to use more secondary raw materialshave been reported in the literature, however.Furthermore, no methodology has been discussedthat would quantitatively assess in what contextthese strategies should be applied.
Several authors, however, have examined theuse of decision-analysis models to improve theeconomic and resource-use performance of re-cycling operations. The most pertinent modelsinclude those that apply a range of mathemati-cal programming techniques to improve decisionsabout raw materials purchasing strategy (Stuartand Lu 2000), technology selection (Kirchainand Cosquer 2007), and the application of up-grading and sorting for secondary raw materi-als (Gaustad et al. 2007; Kirchain and Cosquer2007). Although notionally one can use thesemodels iteratively to evaluate how some changewould affect the ability to use secondary raw ma-terials, none is applicable to evaluating the designof multispecification alloys.
The primary challenge of evaluating therecycling-friendliness of multispecification alloys
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is that it is a context-dependent property; howmuch scrap an alloy can accommodate is based onnot only the compositional characteristics of thealloy itself but also the types of scraps availableto producers, the compositional characteristics ofthose scraps, and their metallic yield. As a result,a method to evaluate recycling-friendliness mustbe able to account for the confluence of thesedetailed effects.
Two sets of previous work on decision-analysismodels have been specifically applied to recyclingperformance of secondary aluminum productionand form the basis for addressing this need. Thefirst set of studies, by Reuter, Van Schaik, andothers (Lund et al. 1994; Shih and Frey 1995;Stuart and Lu 2000; Van Schaik et al. 2002;Van Schaik and Reuter 2004; Reuter et al. 2006;Kirchain and Cosquer 2007), used optimizationmethods and dynamic modeling to optimize therecycling system for end-of-life vehicles, includ-ing the light metals within them. This work andthe models it presents can be used to guide oper-ational and technological decisions by recyclersand to provide reasonable recovery expectationsfor recyclers and, more broadly, policy makers.
The second set of studies is previous work bythe authors (Gaustad and Kirchain 2007) andby Rong and Lahdelma (2006) that describesschematic, mathematical programming modelsthat identify the optimal raw materials mix oneshould blend to produce a given multispecifica-tion alloy or alloy production portfolio. Thesemodels are extensions of batch-planning modelsthat have been developed for decades and areavailable and used within the secondary metalsindustry today. To date, such models have beenused to evaluate the effectiveness of improvedoperational practices and alloy substitution to in-crease potential scrap use. Gaustad and Kirchain(2007) hypothesized that model-derived sensitiv-ity analysis information could be used to directalloy design and demonstrated that, for a stylizedcase, such sensitivity analysis information variedsignificantly across specification and alloy.
This article extends the previous work by(1) characterizing the challenge of develop-ing recycling-friendly alloys due to the contex-tual sensitivity of that property, (2) demon-strating how such decision-support models canbe used to evaluate post facto5 the potential
scrap usage of alloys across a range of raw ma-terials contexts, and (3) exploring the valueof sensitivity analysis information to proac-tively identify the most effective alloy modifi-cation strategies that can drive increased poten-tial scrap use. With regard to (3), this articleextends previous discussions by exploring in de-tail how sensitivity analysis information actuallycorrelates with potential scrap use performanceand how both the sensitivity analysis informa-tion and the associated potential scrap use effectchanges with individual and coordinated specifi-cation modifications. In exploring this sensitivityanalysis for two distinct cases, this article suggeststhat real potential exists for increasing scrap usethrough alloy redesign while remaining withinestablished compositional specifications. Finally,this article extends previous work in this researcharea by presenting a schematic algorithm for ex-plicitly incorporating uncertain metal yield intothe analyses of alloy design specifically and recy-cler operational decisions more broadly.
Both the model and the cases discussed hereinare intended to be schematic in nature. Muchwork still remains to capture the metallurgicalcomplexity of the recycling process; nevertheless,the results presented show that this frameworkholds promise to be a valuable tool in themetallurgist’s tool kit. Furthermore, a recyclingevaluation tool, irrespective of scope or fidelity,is always but a single element in the overall alloydesign process. Traditional and emerging met-allurgical methods are required to identify alloyscapable of meeting demanding physical per-formance requirements. Nevertheless, efficientresource-conscious design of materials dependson analytical tools capable of projecting the im-pact of design choices on recycling performance.
Modeling tools that make use of mathemat-ical programming techniques are broadly avail-able to support the decision making of metallur-gical production planners (Cosquer 2003; Cos-quer and Kirchain 2003). The primary results ofsuch an optimization model are a set of decision
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variables that yield the optimal objective func-tion. In the case of batch-planning tools for sec-ondary alloy production, these decision variablesare the amounts of scrap and primary raw materi-als that can be used to produce the targeted alloys.Later in this article, we use such results directlyto evaluate the ability of specific proposed alloyformulations to be produced from scrap.
Additionally, some optimization models (in-cluding the ones applied in this article) provide apowerful set of results that quantify the sensitivityof the optimal result to changes in assumptions.Among these sensitivity parameters are what areknown as “shadow prices.” A shadow price isdefined for each binding constraint in the op-timization problem, and its value is the change inthe objective function at the optimum for a unitchange in that constraint (de Neufville 1990), asexpressed in equation (1.1). Each shadow pricehas a range of validity associated with it.
SPConstraint = δ(Objective Function)δ(Constraint)
(1.1)
For the model presented subsequently, three po-tential classes of shadow prices are reported.These are shadow prices for (1) constraintson scrap availability, (2) constraints on alloydemand, and (3) constraints on scrap composi-tion. The last are used to provide quantitativeguidance to the design of alloys with improvedrecycling performance. Interested readers shouldconsult work by Gaustad and Kirchain (2007) fora lengthier discussion on the value of the othershadow price analyses for strategic decision mak-ing around secondary materials.
Model Formulation
The first tool needed to improve the recyclingperformance of specific alloys is a method capa-ble of evaluating their potential for secondaryraw materials use across a range of productioncontexts. To accomplish this, in this article weexplore the use of a modified formulation of aschematic model initially described by Gaustadand Kirchain (2007). In particular, the modelexamines the problem of mixing arbitrary quan-tities of raw materials (pure or scrap aluminum)to produce a set of new aluminum alloys un-der certain constraints (e.g., the mixing of raw
materials must meet compositional specificationsfor final products). The goal of this model is toidentify a production plan that minimizes theoverall expected production costs while meet-ing finished good compositional specifications.Generally, this exactly matches at least one setof decisions faced by a batch planner, and suchmodels are prevalent within the secondary metalsindustry. Compared with typical batch-planningtools used in secondary operations today, themodel formulation presented differs primarily inthat it optimizes raw material use across theproduction of an entire portfolio of alloys simul-taneously and allows for key operational uncer-tainties to be explicitly considered in the eval-uation process. It differs substantively from thepresentation in work by Van Schaik and Reuter(2004) and Van Schaik and colleagues (2004);in particular, it comprehends the effects of im-perfect metallurgical yield and allows for thatyield to be represented as an uncertain stochasticparameter.
We specifically developed a model that is ca-pable of treating composition and yield as uncer-tain parameters for three key reasons. First, assess-ments that treat uncertainty implicitly, generallyon the basis of mean expected conditions, as-sume that deviation from that value has symmet-ric consequences. For many production-relateddecisions within the cast-house, the repercus-sions of missing a forecast are inherently nonsym-metrical. Second, deterministic approaches gen-erally do not provide proactive mechanisms tomodify production strategies as prevailing condi-tions evolve. Finally, our previous work (Gaustadand Kirchain 2007) has shown that treating un-certainty explicitly in evaluating recycler opera-tional decisions suggests strategies that improveeconomics and scrap use potential. The mathe-matical formulation of both the core model andthese statistical yield modifications is detailed inSupplement S1 in the Supplementary Materialon the Web.
To check the performance of the batch-planning results generated by the model, weexecuted Monte Carlo simulations that testedthe compositional acceptability of the proposedbatch plan against scraps of varying composition.We carried out these simulations using CrystalBall, an Excel based program.6 The Monte Carlo
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Figure 3 A. Distribution of end-use aluminum shipments (total 9,699,000 metric tons) by category in theUnited States and Canada in 2005. B. Percentages of old aluminum scrap consumed (total 1,154,000 metrictons) in the United States and Canada in 2005 (Plunkert 2005). Elec = electronic; UBC = used beveragecans.
method uses pseudorandom numbers to statisti-cally simulate random variables. For this case,a normal distribution around the compositionalmean of each of the scraps’ elemental consider-ations (silicon [Si], magnesium [Mg], iron [Fe],manganese [Mn], copper [Cu], and zinc [Zn]) wasassumed, and the optimal solution was tested10,000 times. The number of batches that hadany errors (i.e., final composition of finished al-loys fell out of specification) was reported as thebatch error rate (equation 1.2).
error rate =∑
k
∑
j
(1 − αk j ) (1.2)
Applying the ModelingFramework
We used the chance-constrained model in twohypothetical case studies to (1) test its capabil-ity in evaluating the expected recycling perfor-mance of specific proposed “recycling-friendly”alloys from the literature (Das et al. 2007) and(2) demonstrate a framework that utilizes modelresults to guide a priori the design of alloys tofacilitate increased recycling.
Common Data and Assumptions
For both hypothetical case studies describedpreviously, scrap types were selected to be rep-resentative of end-use shipments of aluminumproducts in the United States and Canada. Thelargest categories of applications for aluminumare (1) automotive with minimal aerospace, (2)containers and packaging, and (3) constructionand building materials (see figure 3A). Thesethree categories were used to define the scrapsets that are used in both of the case studies anddetailed in Supplementary Table S2.II in Supple-ment S2 on the Web; specific scraps were selectedfrom publicly available compositional data. Theautomotive scrap set is biased toward automotive-related streams due to the minimal scope of cur-rent aerospace recycling and includes mixed au-tomotive castings; high-copper car radiators; seg-regated alloy 6061 extrusions; and automotiveshredder residue (ASR), which is termed “Zorba”on the scrap market and often has large amountsof impurities. The container and packaging set in-cludes used beverage cans (UBC), thick foil scrap(foil), thin foil scrap (alumifoil), and a segregatedmix of alloys 1100 and 3003. Building and con-struction scraps include mixed aluminum wires
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and cables, segregated alloy 5052 clippings, cleanend-of-life building siding, and segregated alloy6063 architectural extrusions.
Finally, in addition to the three industry-specific scrap sets, a general set of scrap was de-fined to be representative of the overall flow ofscrap in North America. Of the old scrap con-sumed in 2005, UBC, castings, shredded auto-motives, mixed wrought scraps, and extrusionsmade up the majority (viz. figure 3B). The gen-eral scrap set, therefore, was based on a selec-tion of scraps from the three industry-specificscrap sets that closely matched this portfolio.These include UBC, mixed automotive cast-ings, radiators, wire and cable scrap, and mixedturnings.
Compositional data for all scraps were es-timated from European Union (EU) standards(ECS 2003), which are listed in SupplementaryTable S2.I in Supplement S2 on the Web. TheEU standards list maximum compositional spec-ifications under which certain scrap types mustfall; mean scrap compositions were estimated tobe approximately 75% of these values and arelisted by ECS (2003) along with their correspond-ing EU standard number. Nonproprietary infor-mation on the characteristics of available scrapstreams is scarce, partly because of confidential-ity and partly because of variability across theindustry. We worked with several industry ex-perts to devise the data set used in this articlewithout compromising firm-specific information.Although the compositional specifics of any ofthe scrap sets modeled may not match with thoseof scrap sets used by or available to a specific firm,they do represent the diversity of scrap sourcesavailable. We believe that this diversity drives thechallenge of identifying broadly scrap-friendlyalloy improvements.
Prices used in both case studies for primary alu-minum and alloying elements were taken fromthe U.S. Geological Survey (USGS) 2005 av-erages (Plunkert 2005), as shown in Supple-mentary Table S2.V in Supplement S2 on theWeb. We estimated scrap prices from various on-line scrap dealers (LME 2005; GlobalScrap 2007;RecycleNet 2008) by averaging costs of similarlynamed and described scrap categories. Prices varygreatly by day and location, therefore, cost re-sults should be used for relative comparison only.
We assumed that all raw materials were unlim-ited in availability to avoid the potential ef-fects of limited raw materials supplies. The modelframework presented in this article can be usedfor cases of constrained scrap supply with nomodification.
The elemental and gross yield ratios usedsubsequently are given in Tables S2.III throughS2.IV in Supplement S2 on the Web; these wereestimated from EU standards as well as input fromindustry experts. Elements such as silicon andiron have yield ratios higher than 1, as they gen-erally increase due to melt contact with process-ing equipment and refractory. Other elements,including aluminum, have melt loss due to drossand oxide formation, spills, and so forth. It is no-table that only very limited data are collectedcurrently on the specifics of yield loss. Althoughthe figures used in this analysis represent thecollective input of three independent industrysources, researchers should undertake detailed in-quiry to more accurately quantify these values.Nevertheless, incorporating these values in thecase analyses makes it possible to characterize themagnitude of effects attributable to yield-relatedchange.
Within the chance-constrained formulation,the scrap raw materials were modeled with acoefficient of variation (standard deviation di-vided by the mean) of 50% on compositionfor all elements for the base case. Literature onthe variability of aluminum secondary materials(Peterson 1999; Liu 2003) cites coefficients ofvariation (COVs) on elemental means rangingfrom 55% to as high as 3,100%. Sensitivitiesaround this number were also explored. Compo-sitions were assumed to be perfectly uncorrelated.As additional data become available, the implica-tions of this assumption should be explored in fu-ture work. Collectively, this set of data is referredto as the baseline in subsequent discussions.
Case 1: Specific Data and Assumptions
The first case study evaluated three differentalloy sets (R, M1, and M2), each comprisingsix predominant end-market aluminum alloys,one selected from each major alloy series desig-nated by the Aluminum Association (AA). Set Rconsists of recycling-friendly alloys suggested by
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Table 1 Maximum and minimum compositional specifications for finished alloys in weight fraction
Si Mg Fe Cu Mn Zn
Alloy Max Min Max Min Max Min Max Min Max Min Max Min
Note: Recycling-friendly alloys (Set R) are from Das and colleagues (2007), and market alloys sets (M1 and M2) arefrom the Aluminum Association. Si = silicon; Mg = magnesium; Fe = iron; Cu = copper; Mn = manganese; Zn = zinc;Min = minimum; Max = maximum.
Das and colleagues (2007), whereas Set M1 andSet M2 are the currently available market alloysthat most closely match the compositions of SetR. Maximum and minimum compositional con-straints for Sets M1 and M2 are based on interna-tional industry specifications and do not reflectproduction targets of any specific firm; they arefounded on guidelines set by the AA. The compo-sitional constraints for Set R were set by Das andcolleagues (2007). These compositions are listedin table 1. Each set was evaluated for potentialscrap use within the model under conditions thatwould reflect production of 100,000 metric tons(100 kilotons) of each alloy, for a total produc-tion of 600,000 metric tons (600 kilotons). Be-cause the evaluation was carried out under con-ditions with no limitation on the availability ofraw materials, the subsequent results are indepen-dent of production scale. The scale of 100,000metric tons was selected simply for statisticalconvenience.
As outlined in the model formulation section,the batch mixing optimization selects from theset of available scrap, primary aluminum, and al-loying elements to create a mix that meets thecompositional constraints of the alloys produced.Figure 4 summarizes the possible combinations ofboth scrap and alloy sets included in the baselineas described in this case section.
Case 2: Specific Data and Assumptions
For the second case study, we evaluatedtwo alloys, 6063 and 3004, to identify a priorispecification modifications that would improvepotential scrap consumption. We used compo-sitional shadow prices to target which specifica-tions should be modified (i.e., relaxed or tight-ened); we evaluated the subsequent impact onpotential total scrap consumption post facto inthe model.
Mixing DecisionFigure 4 Schematic of possible casestudy combinations for both scrapsavailable and alloy sets produced.R = recycling-friendly alloys; M1 andM2 = market alloy sets.
The first case study evaluated the potential forscrap use (i.e., the recycling-friendliness) withinthe production plan of three different alloy sets(R, M1, and M2), each composed of six predomi-nant end-market aluminum alloys. Set R consistsof recycling-friendly alloys suggested by Das andcolleagues (2007), whereas Set M1 and Set M2are the currently available AA alloys that mostclosely match the compositions of Set R. Set Ralloys are not available and therefore are repre-sented with a letter and alloy series instead of aspecific alloy designation.
Table 2 compares the results for the baselineconditions described above for each of three al-loys sets. Results show a total improvement in po-tential scrap consumption of 67.9% and 65.6%,respectively, with an associated decrease in pri-mary metals purchased, for the recycling-friendlyalloy set (R) over the currently used market alloySets M1 and M2. We evaluated these base casesusing Monte Carlo simulations to have compara-
bly low expected error rates of 0.18%, 0.21%, and0.25%, respectively. The recycling-friendly alloyset shows an associated decrease in modeled pro-duction cost of 13.4% and 13.6% over the otheralloy sets.
Figure 5, however, provides some indicationof the challenge of creating a broadly recycling-friendly alloy. That is, figure 5 shows that thebatch plans for the recycling-friendly alloys out-perform their market counterparts for most (8 of12 alloy comparisons), but not all, of the alloyseries investigated in terms of potential scrap use.Most notable, Alloy C(4XXX) outperforms 4032by 917% and 4045 by 775%; Alloy B(3XXX)outperforms 3005 by 47% and 3004 by 26%. Therecycling-friendly alloys do not outperform all ofthe market alloys, however; Alloy D(5XXX) hasabout the same potential scrap consumption asalloy 5052, whereas Alloy F(7XXX) is outper-formed by both of its comparative market coun-terparts, 7005 and 7075. Later sections explore indetail the source of this underperformance.
Evaluating Recycling Performance:Sensitivity AnalysisThe recycling-friendliness of an alloy is
dependent not only on the compositional
Table 2 Baseline results showing comparison of recycling-friendly alloys (Set R) with current alloys (SetsM1and M2)
Alloy Alloy % � R - Alloy % � R -Set R Set M1 M1 Set M2 M2
Note: M$/kt = million US dollars per kiloton. One kiloton (kt) = 103 tonnes (t) = 103 megagrams (Mg, SI) ≈ 1.102 ×103 short tons. Fifty percent coefficient of variation (COV); total production = 600 kt; α = 99.99% confidence interval.
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Figure 5 General scrap setconsumption comparison forindividual alloy sets, organized byseries (coefficient of variation[COV] = 50%; α = 99.99%confidence interval). Dark shadingindicates data for the alloys of set R;light shading indicates data for thealloys of market alloy sets M1 andM2.
variability of the available scraps but also themake-up of the scrap portfolio itself. Many pro-ducers, depending on the size and location of theirfacility, have access to scrap portfolios that areheavy in scraps from one industry over another.To systematically explore these implications, wetested the three candidate alloy sets against threescrap portfolios, created on the basis of the threemajor aluminum markets shown in figure 3: (1)automotive, (2) containers and packaging, and(3) building and construction. The scrap port-folios, their average compositions, and modeledprices are listed in Supplementary Table S2.II inSupplement S2 on the Web.
As table 3 shows, for each alloy set, theamount of scrap used is highly dependent on the
Table 3 Total scrap material usage (in 1,000 metrictons or kilotons) for the varying scrap portfolios andalloy set combinations
Note: One kiloton (kt) = 103 tonnes (t) = 103 megagrams(Mg, SI) ≈ 1.102 × 103 short tons. Data are ordered bydecreasing scrap utilization by scrap set.
available scrap portfolio. For example, many au-tomotive scraps are shredded and therefore ac-cumulate more iron than other scraps (Gesinget al. 2000). The results confirm expectationsthat this lowers maximum potential usage ofthese scraps compared to other types. Both pack-aging and construction scraps have extremelylow undesirable accumulation and can thereforebe highly utilized. Examining scrap consump-tion by specific alloy (see figure 6A), one cansee an even greater range of usage differences.Market alloys (from Set M1) 7005 and 2014(see figure 6B) accommodate large amounts ofthe construction heavy scrap in their produc-tion portfolios because they are composition-ally close to clean, unpainted siding. Packagingscraps, most notably used aluminum foil, haveextremely low Mg and Mn content and there-fore can be utilized in Alloy 4045. This is inter-esting because the specifications for Alloy 4045mean that it can normally accommodate few tono secondary materials of other scrap types (seefigure 6B).
In the end, the most important observationfrom this analysis is that the available scrap port-folio differentially affects the quantity of scrap useeven for analogous alloys (in the same series). Asa result, the available scrap portfolio can changethe relative performance of any given alloy, in-cluding ones from the recycling-friendly set, com-pared with its analogs in terms of potential scrapuse.
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Figure 6 Recycling-friendly alloy set R (A) and market alloy set M1 (B) scrap use comparison for eachdifferent scrap scenario. Const = construction.
Results in figure 7 indicate that for all three7XXX series alloys, the construction and gen-eral scrap portfolios show the highest usage,with Market alloy 7075 having the potentialto use the most scraps. The automotive andpackaging portfolios show the highest usage forthe recycling-friendly Alloy F(7XXX), althoughtheir overall usages are lower in this alloy thanfor the construction and general scrap sets (seefigure 7). Recycling-friendly Alloy F(7XXX) ismore compositionally restrictive for Mg com-pared with Market alloys 7005 and 7075, whereasMarket alloy 7075 is compositionally more re-
Figure 7 Comparison of scrap used in theproduction portfolio of the 7XXX series alloys foreach of the scrap scenarios. Alloys F(7XXX) and7005 are reproduced from figure 6. Const =construction.
strictive for Fe and Mn compared with therecycling-friendly alloy (see table 1). For theautomotive-heavy scrap portfolio case, one cansee from table 4 that the recycling-friendly al-loy is able to utilize more Zorba and 6061 alu-minum extrusion than Market alloy 7075; thesescraps have fairly high Fe and Mg content. Forthe construction-heavy scrap portfolio case, onecan see that Market alloy 7075 utilizes more wireand cable scrap compared with the other two al-loys. Wire and cable scrap are desirable due totheir low Si content; however, due to their highusage, the Mg becomes the constraining element.Therefore, its Mg specification allows Alloy 7075to accommodate more secondary materials in itsportfolio overall.
Similar results can be shown for the 5XXXalloys. D(5XXX) outperforms its market counter-parts for the automotive-heavy and packaging-heavy scrap portfolios (see figure 8). In thiscase, for the packaging-heavy portfolio, segre-gated 1100/3003 is desirable because it has a lowFe content compared with the other scraps; how-ever, Si becomes a constraining element in theproduction portfolio, and therefore the recycling-friendly alloy can consume more due to its less re-strictive Si specification. Conversely, for the gen-eral and construction-heavy portfolios, althoughAlloys 5052 and D(5XXX) have fairly similar to-tal usage, Alloy 5052 is able to accommodatea very different portfolio of scrap materials. Inparticular, Alloy 5052 has the potential to usemore wire and cable scrap (see table 5) in its
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Table 4 Scrap usage (in 1,000 metric tons or kilotons) for 7XXX series alloys from figure 7 broken downby individual scraps
Automotive set 7XXX 7005 7075 Construction set 7XXX 7005 7075
production portfolio because it is less composi-tionally restrictive in Mg and Mn when comparedwith D(5XXX).
Ultimately, it is apparent that the recyclingperformance of a specific alloy can be stronglydependent on the operational context in whichit is applied. This clearly confounds the processof designing alloys to improve their ability to ac-commodate scrap. Mathematical programming,such as the chance-constrained model used in thisarticle, provides rapid, quantitative insight with-out the need for expensive and time-consumingexperimentation. Nevertheless, given the rangeof potential operational settings (e.g., availablescrap types, compositional variability, raw mate-rial prices) and the continuum of possible com-positional modifications, post facto evaluation,even through a model, may not make effectivealloy design tractable. Instead, the alloy designerneeds insight into what modifications can pro-vide the most benefit. The next section, throughthe examination of a case study, explores the useand value of that information, referred to as a
shadow price, to direct the development of morerecyclable alloys.
Case 2—Designing for ScrapConsumption: Using CompositionalShadow Prices
Although it is clear that modifying alloy spec-ifications could facilitate recycling, the most ef-fective modifications are not easily identified.Unfortunately, the trivial solution of broadeningall compositional specifications is sure to alterthe properties of alloy materials. Instead, the al-loy designer must selectively alter specifications,relaxing some and tightening others, all with-out compromising performance specifications.Case 2 explores the use of model outputs to guidethe a priori modification of alloy specifications toimprove the alloys’ potential for scrap use. Sim-ple examples from Case 1 illustrate the challengeof realizing an effective design in the absence ofsuch guidance.
Figure 8 Comparison of scrap usedin the production portfolio of the5XXX series alloys for each of thescrap scenarios. D(5XXX) and 5454are reproduced from figure 6.Const = construction.
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Table 5 Scrap usage (in 1,000 metric tons or kilotons) for 5XXX series alloys from figure 8 broken downby individual scraps
Packaging set 5XXX 5454 5052 General set 5XXX 5454 5052
Note: UBC = used beverage cans; Cu-Al = copper−aluminum; Seg 1100/3003 = segregated mix of Alloys 1100 and3003.
Consider the relative performance of the4XXX and 5XXX alloys as described in Case 1(i.e., Alloy C had the highest potential for scrapuse of the 4XXX alloys, and 5052 had the high-est potential for scrap use of the 5XXX alloys;see figure 5) and their specifications as shownin figure 9. Figure 9 shows that Alloy C, com-pared with its market-equivalent 4XXX alloys,has a broader specification range for all elements,with the exception of Cu, and a higher maxi-mum specification range for all elements exceptfor Cu and Mg. This is in stark contrast to Al-loy 5052, which, compared with the other 5XXXalloys considered, has the highest potential for
scrap use but neither the broadest nor the highestmaximum specification, with the exception of Fe.These observations reinforce the key challenge ofidentifying the most effective modifications.
With current specifications listing nearly twodozen elements, it is not practical for even fastmodels to iterate through every possible combina-tion of specification modifications. Fortunately,the type of model presented in this article (aswell as those used broadly in industry for dailybatch planning and many other models discussedin the literature), when executed in current opti-mization engines, generates a set of informationthat can direct the design process. As described
Figure 9 Schematic representation of alloy compositional specification windows (in weight fraction) for the4XXX and 5XXX series alloys of all three sets. Constraints for R are set by Das and colleagues (2007), andconstraints for M1 and M2 are set by the Aluminum Association (AA). Si = silicon; Mg = magnesium; Fe =iron; Cu = copper; Mn = manganese; Zn = zinc.
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previously, shadow prices identify those specifica-tions with both the most and the least impact onpotential scrap use. In particular, the magnitudeand sign of the shadow prices on composition in-dicate how the production cost would change ifthe compositional specifications were tightenedor relaxed. Using this information, alloy designerscan implement a prospective framework to sys-tematically and efficiently target alloy specifica-tions for development that provide the most sig-nificant improvements in potential for increasedscrap reuse and reduced production cost. Armedwith such a framework, they should find that thedesign process becomes more efficient.
To explore the value of shadow prices withinthe framework, we investigated modifications totwo specific alloys. These alloys meet the compo-sitional specification of 6063 and 3004, as shownin table 1. To allow for alloy modifications thatinvolve both tightening and relaxing specifica-tions but still remain within the AA specification,we carried out the base case assessment with themost constraining specification (by coincidence,Mg in both cases) set to 10% of the width listedin table 1. This width reduction provides us theopportunity to explore constraint relaxing; andwe carried it out by changing only the maximumspecification (the more binding specification7).For example, for the analysis of 6063, the baselinemaximum specifications were set to the values aslisted in table 1, except for Mg, which was set toεmin + 10%(εmax − εmin) = 0.0049 weight frac-tion.8 We refer to these alloys in the subsequentdiscussions as 6063sr for specification restricted.By establishing these alloys as a baseline for com-parison, we can make all of the subsequent mod-ifications without causing the resultant alloy tofall outside of AA specifications.
Table 6 shows the shadow prices for the maxi-mum specification constraints for original Alloys6063 and 3004 and Alloys 6063sr and 3004sr. Thelargest shadow prices indicate the alloys with thelargest potential effect on production cost and,therefore, potential scrap use. For Alloy 6063sr,the largest compositional shadow price is that as-sociated with the maximum specification for Mgat $808/weight fraction change. On the basis ofthis information, one would therefore propose arecycling-friendly alloy with a relaxed constrainton Mg. Such an alloy would be the same as Mar-
Table 6 Compositional shadow prices (USdollars/weight fraction change) for maximumspecifications for 6063 (from Set M1) and 3004(from Set M2) as well as their specification restricted(sr) versions
Note: Mg = magnesium; Si = silicon; Fe = iron; Cu =copper; Mn = manganese; Zn = zinc.
ket alloy 6063, but with the compositional con-straints on maximum Mg composition modifiedslightly. In particular, figure 10A shows the im-plications of relaxing this specification from avalue of 0.0049 weight fraction (i.e., 10% of thefull listed AA specification window) to 0.0090weight fraction (95% of the full window). Ex-panding this specification over this range resultsin a 16-fold increase in potential scrap utilization.Increasing the specification beyond the AA spec-ification could result in even higher scrap utiliza-tion; however, these changes may be less feasibledue to processing and property restrictions.
It is intuitive that relaxing compositional con-straints makes it possible for an alloy to accom-modate more scrap in its optimal productionportfolio. To maintain properties, however, onewould likely need to accommodate this relaxationthrough the tightening of other specifications.Compositional shadow prices also indicate whichof the constraints could be tightened with theleast effect on potential scrap utilization. In thiscase, the lowest shadow prices indicate the con-straints with the least effect on cost and, there-fore, scrap usage.
We use figure 10B to explore the implica-tions of complementary tightening of constraints.Within figure 10B, each curve represents theimpact of constraint tightening overlaid on theimpact of Mg constraint relaxing from the plotabove. As with figure 10A, we tighten the con-straints here by only modifying the maximum
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Figure 10 A. Improvement in potential scrap consumption from relaxing magnesium (Mg) constraints onAlloy 6063 from 10% to 95% of as-listed Aluminum Association (AA) specification width. A given percentageon the x-axis translates into a Mg specification through the relationship εmax = εmin + X%(εmax − εmin). B.Effect on scrap consumption of overlaying a tightening of other constraints in conjunction with relaxing theMg constraint corresponding to the same value on the x-axis of the graph above (figure 10A). The maximumspecification of a given element on a specific plot follows, εmax = εmax − X%(εmax − εmin). The dashed linerepresents the effect of tightening all other specifications (silicon [Si], iron [Fe], copper [Cu], manganese [Mn],and zinc [Zn]) in conjunction with relaxing the Mg constraint by an equal percentage amount.
specification for the given alloying element, witha percentage tightening of X% translating to aspecification value of εmax – X%(εmax − εmin).For example, the height of the solid black curveat 60% on the x-axis represents the change inpotential scrap usage associated with a concur-rent 60% tightening of the Si and Zn constraintson top of the 60% relaxation of the Mg con-straint captured in figure 10A above. Similarly,the height of the gray solid line at 40% repre-sents the change in potential scrap use associ-ated with a 40% tightening of the Fe constraintin addition to a 40% relaxation of the Mg con-straint. Obviously, specific alloy modifications donot have to mirror one another and could takeon any given value. We chose this presentationstrategy to densely represent the range of possiblealloy modifications that could improve potential
scrap usage when such modifications are selectedcarefully.
Reviewing the compositional shadow pricesin table 6, one would expect that the specifi-cations on Si, Zn, and Fe for 6063sr could betightened with little negative impact on scrapusage. Figure 10B shows that this hypothesis iscorrect for specification tightening of 0% to 40%for Fe and 0% to 60% for both Si and Zn. Tight-ening the Fe specification beyond 40% beginsto compromise the ability to use scrap. Simi-larly, tightening beyond 60% for Si and Zn be-gins to have a significant reduction on scraputilization.
This analysis suggests that it should be pos-sible to use shadow price information to iden-tify effective alloy modification targets. Theexistence of the inflection points in each of the
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Figure 11 Framework to identifyalloy modification targets andpossible recycling-friendly alloys.
constraint tightening curves (see figure 10B) re-flects the fact that all specifications, even oneswith very low shadow prices, can eventually be-come a limitation to scrap use. To avoid explor-ing alloy modifications that involve constraintstightened to the extent that scrap use is com-promised, we must employ an iterative procedureof using shadow prices and model evaluation (aswell as technical performance evaluation). As di-agrammed in figure 11, this procedure involvesexecuting the model described here or a similarbatch-planning model (c) for an alloy of interest(a) and a broad set of available secondary materi-als (b). This model execution will generate bothan optimal production plan and shadow pricesfor the compositional specifications. The alloyproducer can use those shadow prices to identifyspecifications that are candidates to modify to in-crease scrap use (d) and to compensate for those
modifications through tightening without com-promising scrap use (e). The producer can testpromising specification modifications (f) withinthe model to understand the extent of scrap useimprovement (g). This step is particularly impor-tant for any proposed compensatory constrainttightening to ensure that the amount of tighten-ing does not reach a point that undermines othergains (h). New alloy specifications would eventu-ally need to be tested for technical performance(h), a procedure that lies outside of this method.Ideally, an alloy producer could iterate new al-loys with satisfactory performance through thisprocess again to see whether further scrap usageimprovements were possible (j—yes). This itera-tive process could identify a set of promising alloycandidates, and the alloy producer would selectfrom the set that met performance requirements(j—no).
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We use a second example to demonstratesuch an approach more directly. One of the pro-posed recycling-friendly alloys that did not in-crease scrap usage for every scrap type was AlloyB(3XXX); this is a case in which the market al-loy could accommodate more scrap than the pro-posed recycling-friendly alloy in some instances.By looking at the compositional shadow priceson the maximum specifications for the 3XXX se-ries market alloys (cf. table 6), one can see thatMg again has the highest shadow prices for Alloy3004sr, with a value of 222.7, 30 times larger thanthe next largest value, for Si. One would there-fore propose design of a recycling-friendly alloywith relaxed constraints on Mg.
Figure 12A shows the results of executingthe model for modifications of the Alloy 3004sr,which involve relaxing the maximum specifica-tion on Mg from the baseline value of 0.85 weightpercentage (wt%) to 1.3 wt% (a relaxation ofthe constraint window by 50%). Given the largeshadow price, it is not surprising that expandingthe Mg specification across this range results ina nearly 40-fold increase in potential scrap uti-lization. For illustration purposes, we select analloy modification halfway through this range,at 25% relaxation. As a crude way of trackingthe metallurgical implications of this and sub-sequent proposed modifications, it is useful tolook at the minimum expected aluminum con-tent within the alloy. If we increased the widthof the Mg specification window by 25%, the min-imum aluminum content would drop from 96.15wt% to 95.95 wt%. It is likely that we would needto compensate for this change by tightening otherspecifications.
Examining the shadow prices for the modifiedalloy, labeled 3004sr′′ in figure 12B, one hypothe-sizes that tightening the constraint on Mn wouldhave the smallest effect on scrap usage. The plotin figure 12B shows the results of testing mod-ifications to the Mn specifications for 3004sr′′
and reveals a broad range over which one cantighten the constraint on Mn without compro-mising scrap usage in the alloy. In fact, the widthof the constraint can be reduced to a value only2% of the original width (98% tightening on theplot) before scrap usage falls below the level ofthe baseline 3004sr specification. For illustrativepurposes, we select a value of 50% tightening,
which results in a Mn specification of 1.25 wt%for proposed Alloy 3004sr′′. Such a change wouldlead to a minimum aluminum content of 96.2wt% in 3004sr′′.
As a final example of iteration, looking at theshadow prices for 3004sr′′ reveals that, of the otherspecifications, Cu has the lowest shadow priceand therefore represents a promising candidatefor modification. As for Mn, executing the modelfor Cu constraint modifications on 3004sr′′ con-firms this expectation, with only small reductionsof potential scrap use for window tightening upto nearly 90%. Using this information and fol-lowing the pattern above, one could propose afinal alloy modification 3004sr′′′ at 50% windowtightening for Cu, a point that translates into amaximum specification of 0.13 wt% Cu. At thispoint, minimum aluminum content would sit at96.33%, and potential scrap usage would haveclimbed to 18% (from a value of 1% for 3004sr).
We provide these examples to illustrate how aproperly constructed batch-planning model andthe shadow price information that it could gener-ate can be used to inform the alloy design process.These examples also demonstrate that, for mostproduction constructs, there are compositionalconstraints with both large (Mg for 6063 and3004) and small (e.g., Si, Zn, and Fe for 6063;Mn and Cu for 3004) shadow prices. Any ac-tual alloy design process should also be informedby metallurgical considerations concerning thecomplementary (or conflicting) effects of variousalloying elements.
In the end, shadow prices provide valuable in-formation on which elemental specification mod-ifications may have the largest impact on scrapuse (both positive and negative). The large num-ber of elemental considerations of today’s alu-minum alloys, coupled with the often volatilestate of the secondary materials market, makes al-loy design for recycling an increasingly complexand challenging task. The model presented inthis article aids the alloy designer by consideringboth the compositional uncertainty of secondarymaterials and the impact that their use has onan alloy’s ability to be produced from scrap. Thesensitivity analysis that accompanies the optimalproduction portfolio solutions can guide design-ers in terms of targeting which specification con-straints could be relaxed or tightened.
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Figure 12 A. Improvement in scrap consumption from relaxing magnesium (Mg) constraints on Alloy3004. B. Effect on scrap consumption of now tightening manganese (Mn) constraint. C. Effect on scrapconsumption of now tightening copper (Cu) constraints. D. New maximum specifications for 3004sr ′ ′′ . Maxspec = maximum specification; SP = shadow price; Si = silicon; Fe = iron; Zn = zinc; Cu = copper; Min =minimum.
Conclusions
Growing industrial awareness of resourcescarcity and environmental impact has high-
lighted the steadily increasing consumption ofmetals and materials in production. A key strat-egy for enabling a shift to more sustainable useof materials is increased recycling. Although
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reaching full recycling potential will likely re-quire changes throughout any given materials sys-tem, one strategy that may play an important roleis the redesign of alloys to accommodate morescrap. Realizing such redesign will require effec-tive tools to evaluate an alloy’s potential to makeuse of more scrap; without such tools, redesigncan only proceed by expensive trial and error.
This article has explored the use of a modelingframework, specifically a chance-constrained op-timization framework, as such a tool to (1) eval-uate an alloy’s ability to accommodate recycledmaterials (scrap) in its production portfolio and(2) proactively identify the most effective alloymodification strategies that can drive increasedpotential scrap use. Additionally, this article ex-tends our previous work (Gaustad and Kirchain2007) by presenting a schematic algorithm for ex-plicitly incorporating uncertain metal yield intothe analyses of alloy design specifically and recy-cler operational decisions more broadly.
In Case 1, the model was shown to be effec-tive at differentiating the potential scrap usage ofa set of suggested recycling-friendly alloys particu-larly as production context shifted across differentscraps sets. The specifications for these alloys, assuggested in the literature, were generally shownto enable increased scrap usage, although this im-provement was not uniform across all alloy series.This improvement in secondary material utiliza-tion was shown to be context dependent on boththe product the alloy is replacing as well as thescraps that are available for its production.
In Case 2, the optimization framework wasalso shown to be useful in guiding the initial alloydesign process in regard to which compositionalspecifications an alloy designer should target formodification to increase recyclability. With re-spect to guiding such a design process, this ar-ticle extends previous discussions (Kirchain andCosquer 2007) by exploring in detail how sen-sitivity analysis information actually correlateswith potential scrap use performance and howboth the sensitivity analysis information and theassociated potential scrap use effect changes withindividual and coordinated specification modifi-cations. The case analyses suggest that real poten-tial exists for increasing possible scrap use throughalloy redesign while remaining within establishedcompositional specifications.
Both the model and the cases discussed in thisarticle are intended to be schematic in nature.Much work still remains to capture the metal-lurgical complexity of the recycling process; nev-ertheless, the results presented show that such aframework holds promise to be a valuable partof the metallurgist’s tool kit. This is especiallyimportant because evaluating all possible specifi-cation combinations is not practical for efficientdecision making. In addition to being highly ef-ficient, this method makes use of a type of modelcurrently in place for aluminum batch planningand therefore could be implemented without ad-ditional capital investment. In the end, that de-sign process is still dependent on traditional andemerging methods to identify alloys that willsatisfy demanding physical performance require-ments. Nevertheless, efficient design of materialsrequires resource-conscious analytical tools thatare capable of projecting the impact of designchoices on recycling performance.
Acknowledgements
We acknowledge the help and support ofAleris International, Alcoa Primary Metals, andHydro Aluminum. Collaborators in the Mate-rials Systems Lab, including Rich Roth andFrank Field, were also key in making this projectsuccessful.
Notes
1. One megajoule (MJ) = 106 joules (J, SI) ≈ 239 kilo-calories (kcal) ≈ 948 British Thermal Units (BTU).One kilogram (kg, SI) ≈ 2.204 pounds (lb).
2. The Aluminum Association designates specific al-loys by their major alloying elements using a four-digit code for wrought aluminum alloys and a three-digit code for cast aluminum alloys.
3. Wrought and cast refer to the specific processingtechnique used to produce the aluminum; wroughtproducts are physically worked into their final shape,whereas cast products are melted, introduced into amold, and allowed to solidify into the mold shape.
4. Many nontechnological strategies are as importantas (or more important than) the technological oneslisted and discussed here. Two of note are educationto encourage increased consumer participation andpolicy that is consistent with societal goals aroundsustainable materials use.
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5. Post facto here refers to the time after alloy design iscomplete—that is, when a compositional specifica-tion has been set but still before actual production.
6. See www.oracle.com/technology/products/bi/crystalball/index.html.
7. It is no surprise that, for a model that either mini-mizes raw material cost or maximizes scrap use, moreof the binding compositional constraints are maxi-mums (e.g., 30 of 52 for the recycling-friendly alloyset); the amount of contaminants in a scrap usu-ally determines how much dilution with primaryaluminum is required and is therefore the majorlimiting factor. The shadow prices on magnesium,copper, and manganese are typically higher becausethese three alloying elements are the most expen-sive (more than $2,000/tonne in the cases studied inthis article) and therefore have the highest impacton the production cost.
8. Where εmax−εmin is the finished alloy specificationwindow.
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About the Authors
Gabrielle Gaustad was a graduate student inthe Department of Material Science and Engi-neering at the Massachusetts Institute of Tech-nology (MIT) in Cambridge, Massachusetts, atthe time this article was first submitted. She iscurrently assistant professor in the Golisano In-stitute for Sustainability at the Rochester Insti-tute of Technology in Rochester, New York. ElsaOlivetti is a research scientist in the MaterialsSystem Lab at MIT. Randolph Kirchain is an as-sociate professor in the Engineering Systems Di-vision and the Department of Material Scienceand Engineering at MIT.
Supplementary Material
Additional Supplementary Material may be found in the online version of this article:
Supplement S1. This supplement contains the mathematical formulation incorporating yieldinto the chance-constrained optimization framework.
Supplement S2. This supplement contains tables with the data used for the case studies presentedin this article.
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